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Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.
This report documents the full details of the condensed journal article by Ashpis & Reshotko (JFM, 1990) entitled "The Vibrating Ribbon Problem Revisited." A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (JFM, 1965) is modified by application of the Briggs method and a careful treatment of the complex double Fourier transform inversions. Expressions are obtained in a natural way for the discrete spectrum as well as for the four branches of the continuous spectra. These correspond to discrete and branch-cut singularities in the complex wave-number plane. The solutions from the continuous spectra decay both upstream and downstream of the ribbon, with the decay in the upstream direction being much more rapid than that in the downstream direction. Comments and clarification of related prior work are made.
Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.
Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.
The inversion method provides a quantitative evaluation of the trade-off between vertical resolution of a retrieved profile and formal root-mean-square (rms) error due to measurement noise propagation. The problem of retrieving the top-side ozone profile from backscattered ultraviolet (BUV) measurements is considered. For measurements of the type currently being obtained with the Nimbus 4 and AE-E BUV experiments, it is found that a vertical resolution of approximately 0.75 scale height can be achieved for a formal volume mixing ratio profile error of 10%. Other examples include treatments of the retrieval of temperature profiles from measurements in the 15 micron CO2 absorption band for both the terrestrial and Martian atmospheres. Finally, the method is applied to the problem of retrieving temperature profiles of the Jovian planets from measurements in the far infrared pressure induced H2 lines to be obtained from the Mariner Jupiter/Saturn fly-by missions.
An efficient numerical technique for the eigenvalue solution in the free vibration analysis of compressible fluid-structure coupled systems is presented. The fluid is assumed to be compressible in nature and the incompressible problem is only a special case of the present generalized algorithm. A natural frequency analysis of the structure in the absence of any fluid is achieved by a combined Sturm sequence and inverse iteration technique that computes only the required eigenvalues and vectors. A special inverse iteration scheme is then developed for the coupled system that uses the computed eigenvalues as starting iteration values for convergence. Numerical results obtained by solving a number of standard test cases indicate the pattern of root convergence corresponding to various simplifying assumptions.
Problems encountered in the definition of relevant parameters which can describe heterogeneous media as a whole are discussed. A procedure to extend the definition of parameters from local to regional scales via inversion of appropriate models is tentatively proposed. The adequacy of these models for describing physical processes at the earth/atmosphere interface as observed with satellite systems is addressed.
The results are presented of a stress intensity factor analysis of semicircular surface cracks in the inner raceway of an engine bearing. The loading consists of a moving spherical Hertzian contact load and an axial stress due to rotation and shrink fit. A 3-D linear elastic Boundary Element Method code was developed to perform the stress analysis. The element library includes linear and quadratic isoparametric surface elements. Singular quarter point elements were employed to capture the square root displacement variation and the inverse square root stress singularity along the crack front. The program also possesses the capability to separate the whole domain into two subregions. This procedure enables one to solve nonsymmetric fracture mechanics problems without having to separate the crack surfaces a priori. A wide range of configuration parameters was investigated. The ratio of crack depth to bearing thickness was varied from one-sixtieth to one-fifth for several different locations of the Hertzian load. The stress intensity factors for several crack inclinations were also investigated. The results demonstrate the efficiency and accuracy of the Boundary Element Method. Moreover, the results can provide the basis for crack growth calculations and fatigue life prediction.
This paper describes an investigation into the structure of representations of sets of actions, utilizing semigroup theory. The goals of this project are twofold: to shed light on the relationship between tasks and representations, leading to a classification of tasks according to the representations they admit; and to develop techniques for automatically transforming representations so as to improve problem-solving performance. A method is demonstrated for automatically generating serial algorithms for representations whose actions form a finite group. This method is then extended to representations whose actions form a finite inverse semigroup.
This paper discusses certain aspects of a new inversion based algorithm for the retrieval of rain rate over the open ocean from the special sensor microwave/imager (SSM/I) multichannel imagery. This algorithm takes a more detailed physical approach to the retrieval problem than previously discussed algorithms that perform explicit forward radiative transfer calculations based on detailed model hydrometer profiles and attempt to match the observations to the predicted brightness temperature.
The question of how random, or unconstrained, paleobiologic models should be is examined with a case study: Signor's (1982, 1985) inverse calculation of levels of marine species diversity through the Phanerozoic. His calculation involved an ingenious model that estimated species numbers and species abundances in the world oceans of the past by correcting known numbers of fossil species for variations in sedimentary rocks available for sampling and in effort paleontologists might devote to sampling. The model proves robust to changes in possible shapes of species-abundance distributions, but it is sensitive to alterations in the assumption that paleontologists collect fossils at random. If it is assumed that ease of collecting varies with age of sediment (with the Cenozoic offering easy sampling) or that paleontologists tend to seek out rarer fossils, results of the inverse calculation change. In particular, the magnitude of the calculated Cenozoic diversity increase always declines from the factor of about seven as originally reported to something considerably smaller. This leaves open the problem of the magnitude of Cenozoic increase in marine species diversity, awaiting better empirical data and, perhaps, more exacting models, random or otherwise.
Oman - The early mission operational problems caused by space motion sickness have been largely resolved in recent years. This has been achieved by appropriate timeline adjustments, voluntary head movement restriction, and judicious use of promethazine. Crew members now simply accept that some symptoms "come with the job," and usually last only a few days. But as more people have flown longer flights, we've seen cases of space sickness and inversion illusion that take several weeks to resolve. Visual reorientation illusions continue throughout long flights, and occasionally cause difficulties. EVA astronauts sometimes suddenly fear they will fall out of the payload bay or off of the RMS or Strella arms. Orientation and navigation in three dimensions in the MIR station reportedly does not come naturally, because modules have different visual verticals. It is clear that the neurovestibular problems of spaceflight have not disappeared. After return to Earth, many crew members are disoriented and ataxic in the first hour after return, and require assistance leaving the vehicle, Flight surgeons say that the longer the mission, the stronger the aftereffects, certain of which last for weeks. We do not yet know how to predict who will be afflicted. Looking ahead to 3-4 month long voyages to Mars, it seems obvious that if cruise is in O-G, the crew may encounter neurovestibular problems on arrival. Artificial G may be broadly effective as a countermeasure for many of the physiological changes of spaceflight, but from the neurovestibular perspective, it is a double-edged sword. We know that the Coriolis stimulus resulting from rotation is potentially disorienting and nauseogenic. But we don't yet know how much artificial G will be enough, nor how successfully people can adapt to a specific angular velocity and hypo G level. Development of countermeasures remains a big challenge for our neurovestibular community. Maintaining an interdisciplinary perspective is important. Three examples were presented at this meeting: 1) Transgenic animal experiments suggest that in addition to the light illumination cycle, vestibular inputs may also serve as an important input to the circadian system. 2) Radiation can cause important CNS effects in animals, including loss of spatial memory. 3) As described in our session, otolith inputs may contribute to cardiovascular regulation of orthostatic tolerance. Over the past three days, we've all enjoyed catching up with old friends, and making many new ones. On behalf of my colleagues, I want to thank Al Coats and the USRA DSLS staff for the great job they did in running this meeting. And keeping the emphasis on fun. And also my Co- Chair, Mal Cohen, who had more stamina than many of us, despite major surgery only three weeks ago. Mal and I have written a few lines describing each of the seventeen papers in our session, to give you a quick over-view, and as a guide to the full abstracts, We have grouped them under five themes: preflight and inflight countermeasurements, postlanding posture and locomotion deficits: assessment and prediction, adaptive processes, relationships among physical simuli, perceptions, and eye movements, vestibular contribution to human autonomic responses, and implications and recommendations.
The spectrum of cosmic ray electrons above 10 GeV was studied extensively. The spectrum is predicted to steepen at an energy which is related to the lifetime of electrons in the interstellar medium against losses due to inverse Compton collisions with photons and to synchrotron radiation in galactic magnetic fields. The experimental results diverge widely; the lack of agreement between the various measurements is due to a variety of experimental problems.
The structure, composition, dynamics and energy balance of planetary upper atmospheres through interpretation of steller occultation data from Uranus is discussed. The wave-optical problem of modelling strong scintillation for arbitrary turbulent atmospheres is studied, as well as influence of turbulence. It was concluded that quasi-global features of atmospheric structure are accurately determined by numerical inversion. Horizontally inhomogeneous structures are filtered out and have little effect on temperature profiles.
A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed optimization technique which uses a piecewise polynomial representation for the state and controls, and collocation, thus converting the optimal control problem into a nonlinear programming problem, which is solved numerically. This technique has been modified to provide efficient handling of those portions of the trajectory which can be determined analytically, i.e., the coast arcs. Among the problems that have been solved using this method are optimal rendezvous and transfer (including multirevolution cases) and optimal multiburn orbit insertion from hyperbolic approach.
The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter (PVO) by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter was evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.
The application of thin film technology to the vacuum ultraviolet (VUV) wavelength region from 120 nm to 230 nm has not been fully exploited in the past because of absorption effects which complicate the accurate determination of the optical functions of dielectric materials. The problem therefore reduces to that of determining the real and imaginary parts of a complex optical function, namely the frequency dependent refractive index n and extinction coefficient k. We discuss techniques for the inverse retrieval of n and k for dielectric materials at VUV wavelengths from measurements of their reflectance and transmittance. Suitable substrate and film materials are identified for application in the VUV. Such applications include coatings for the fabrication of narrow and broadband filters and beamsplitters. The availability of such devices open the VUV regime to high resolution photometry, interferometry and polarimetry both for space based and laboratory applications. This chapter deals with the optics of absorbing multilayers, the determination of the optical functions for several useful materials, and the design of VUV multilayer stacks as applied to the design of narrow and broadband reflection and transmission filters and beamsplitters. Experimental techniques are discussed briefly, and several examples of the optical functions derived for selected materials are presented.
Accurate determination of spatial soil moisture distribution and monitoring its temporal variation have a significant impact on the outcomes of hydrologic, ecologic, and climatic models. Development of a successful remote sensing instrument for soil moisture relies on the accurate knowledge of the soil dielectric constant (epsilon(sub soil)) to its moisture content. Two existing methods for measurement of dielectric constant of soil at low and high frequencies are, respectively, the time domain reflectometry and the reflection coefficient measurement using an open-ended coaxial probe. The major shortcoming of these methods is the lack of accurate determination of the imaginary part of epsilon(sub soil). In this paper a microstrip ring resonator is proposed for the accurate measurement of soil dielectric constant. In this technique the microstrip ring resonator is placed in contact with soil medium and the real and imaginary parts of epsilon(sub soil) are determined from the changes in the resonant frequency and the quality factor of the resonator respectively. The solution of the electromagnetic problem is obtained using a hybrid approach based on the method of moments solution of the quasi-static formulation in conjunction with experimental data obtained from reference dielectric samples. Also a simple inversion algorithm for epsilon(sub soil) = epsilon'(sub r) + j(epsilon"(sub r)) based on regression analysis is obtained. It is shown that the wide dynamic range of the measured quantities provides excellent accuracy in the dielectric constant measurement. A prototype microstrip ring resonator at L-band is designed and measurements of soil with different moisture contents are presented and compared with other approaches.